This review paper provides an overview of complexity-based analysis techniques in biomedical image analysis, examining their theoretical foundations, computational methodologies, and practical applications across various medical imaging modalities. Through a synthesis of relevant literature, we explore the utility of complexity-based metrics such as fractal dimension, entropy measures, and network analysis in characterizing the complexity of biomedical images (e.g. magnetic resonance imaging (MRI), computed tomography (CT) scans, X-ray images). Additionally, we discuss the clinical implications of complexity-based analysis in areas such as cancer detection, neuroimaging, and cardiovascular imaging, highlighting its potential to improve diagnostic accuracy, prognostic assessment, and treatment outcomes. The review concludes that complexity-based analysis significantly enhances the interpretability and diagnostic power of biomedical imaging, paving the way for more personalized and precise medical care. By elucidating the role of complexity-based analysis in biomedical image analysis, this review aims to provide insights into current trends, challenges, and future directions in this rapidly evolving field.